Is it possible to implement a script into a multiplayer map that makes one team bump possess elites so that we can play spartans vs elites?

You would have cyborg bodies everywhere as well as stationary elite bipeds,

No. Only the server can bump possess.

Everybody can when it's enabled, it's just to glitchy to be actually usefull like non syncing, so it's a 'no' but it is possible technically, but not usefull at all.
This is the same topic about different colours or bipeds for the other team just in other context, it's not possible except if you want to use it for machinima then it's just some workarounds to trick people in it.

you forgot to turn it off and you exceptioned?
the client should exception, not the host.
if the host bumps a client, you will wander around in it without being able to control it for some time, then the client crashes if he won't bump something for you to jump over in, and you gain control of the client's body.

I already had a topic about that some time ago, died out for some reason so can't be good.
I had that idea for spawning you in midair so that you trigger in it, then get out of it, but for some reason there is something with the permutations

how does it know when people are respawning? anyone who walks into the trigger will become elites.

Have the trigger volumes in a certain area, and upon entering you switch permutations and are teleported to the 'real' starting point. I think this is what Jay's doing for SWMT, for the AT-At's specifically.

How does different bipeds have to with our AT AT?

They though that you guys were gonna do that. Anyway, ill try what Lone Warrior said.
And post a pic for April Fools